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<div class="fragment"><div class="line"><a name="l00001"></a><span class="lineno">    1</span>&#160;<span class="comment">/* ----------------------------------------------------------------------</span></div>
<div class="line"><a name="l00002"></a><span class="lineno">    2</span>&#160;<span class="comment">    CFDEMcoupling - Open Source CFD-DEM coupling</span></div>
<div class="line"><a name="l00003"></a><span class="lineno">    3</span>&#160;<span class="comment"></span></div>
<div class="line"><a name="l00004"></a><span class="lineno">    4</span>&#160;<span class="comment">    CFDEMcoupling is part of the CFDEMproject</span></div>
<div class="line"><a name="l00005"></a><span class="lineno">    5</span>&#160;<span class="comment">    www.cfdem.com</span></div>
<div class="line"><a name="l00006"></a><span class="lineno">    6</span>&#160;<span class="comment">                                Christoph Goniva, christoph.goniva@cfdem.com</span></div>
<div class="line"><a name="l00007"></a><span class="lineno">    7</span>&#160;<span class="comment">                                Copyright 2009-2012 JKU Linz</span></div>
<div class="line"><a name="l00008"></a><span class="lineno">    8</span>&#160;<span class="comment">                                Copyright 2012-     DCS Computing GmbH, Linz</span></div>
<div class="line"><a name="l00009"></a><span class="lineno">    9</span>&#160;<span class="comment">-------------------------------------------------------------------------------</span></div>
<div class="line"><a name="l00010"></a><span class="lineno">   10</span>&#160;<span class="comment">License</span></div>
<div class="line"><a name="l00011"></a><span class="lineno">   11</span>&#160;<span class="comment">    This file is part of CFDEMcoupling.</span></div>
<div class="line"><a name="l00012"></a><span class="lineno">   12</span>&#160;<span class="comment"></span></div>
<div class="line"><a name="l00013"></a><span class="lineno">   13</span>&#160;<span class="comment">    CFDEMcoupling is free software; you can redistribute it and/or modify it</span></div>
<div class="line"><a name="l00014"></a><span class="lineno">   14</span>&#160;<span class="comment">    under the terms of the GNU General Public License as published by the</span></div>
<div class="line"><a name="l00015"></a><span class="lineno">   15</span>&#160;<span class="comment">    Free Software Foundation; either version 3 of the License, or (at your</span></div>
<div class="line"><a name="l00016"></a><span class="lineno">   16</span>&#160;<span class="comment">    option) any later version.</span></div>
<div class="line"><a name="l00017"></a><span class="lineno">   17</span>&#160;<span class="comment"></span></div>
<div class="line"><a name="l00018"></a><span class="lineno">   18</span>&#160;<span class="comment">    CFDEMcoupling is distributed in the hope that it will be useful, but WITHOUT</span></div>
<div class="line"><a name="l00019"></a><span class="lineno">   19</span>&#160;<span class="comment">    ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or</span></div>
<div class="line"><a name="l00020"></a><span class="lineno">   20</span>&#160;<span class="comment">    FITNESS FOR A PARTICULAR PURPOSE.  See the GNU General Public License</span></div>
<div class="line"><a name="l00021"></a><span class="lineno">   21</span>&#160;<span class="comment">    for more details.</span></div>
<div class="line"><a name="l00022"></a><span class="lineno">   22</span>&#160;<span class="comment"></span></div>
<div class="line"><a name="l00023"></a><span class="lineno">   23</span>&#160;<span class="comment">    You should have received a copy of the GNU General Public License</span></div>
<div class="line"><a name="l00024"></a><span class="lineno">   24</span>&#160;<span class="comment">    along with CFDEMcoupling; if not, write to the Free Software Foundation,</span></div>
<div class="line"><a name="l00025"></a><span class="lineno">   25</span>&#160;<span class="comment">    Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA</span></div>
<div class="line"><a name="l00026"></a><span class="lineno">   26</span>&#160;<span class="comment"></span></div>
<div class="line"><a name="l00027"></a><span class="lineno">   27</span>&#160;<span class="comment">Description</span></div>
<div class="line"><a name="l00028"></a><span class="lineno">   28</span>&#160;<span class="comment">    This code is designed to realize coupled CFD-DEM simulations using LIGGGHTS</span></div>
<div class="line"><a name="l00029"></a><span class="lineno">   29</span>&#160;<span class="comment">    and OpenFOAM(R). Note: this code is not part of OpenFOAM(R) (see DISCLAIMER).</span></div>
<div class="line"><a name="l00030"></a><span class="lineno">   30</span>&#160;<span class="comment">    </span></div>
<div class="line"><a name="l00031"></a><span class="lineno">   31</span>&#160;<span class="comment">    Copyright of this contribution:</span></div>
<div class="line"><a name="l00032"></a><span class="lineno">   32</span>&#160;<span class="comment">    Copyright 2014-     TU Graz, IPPT</span></div>
<div class="line"><a name="l00033"></a><span class="lineno">   33</span>&#160;<span class="comment">------------------------------------------------------------------------- */</span></div>
<div class="line"><a name="l00034"></a><span class="lineno">   34</span>&#160;</div>
<div class="line"><a name="l00035"></a><span class="lineno">   35</span>&#160;<span class="preprocessor">#ifndef CFDEM_MATH_EXTRA_H</span></div>
<div class="line"><a name="l00036"></a><span class="lineno">   36</span>&#160;<span class="preprocessor"></span><span class="preprocessor">#define CFDEM_MATH_EXTRA_H</span></div>
<div class="line"><a name="l00037"></a><span class="lineno">   37</span>&#160;<span class="preprocessor"></span></div>
<div class="line"><a name="l00038"></a><span class="lineno">   38</span>&#160;<span class="preprocessor">#include &lt;vector&gt;</span></div>
<div class="line"><a name="l00039"></a><span class="lineno">   39</span>&#160;<span class="comment">//#include &quot;math.h&quot;</span></div>
<div class="line"><a name="l00040"></a><span class="lineno">   40</span>&#160;<span class="preprocessor">#include &quot;stdio.h&quot;</span></div>
<div class="line"><a name="l00041"></a><span class="lineno">   41</span>&#160;<span class="preprocessor">#include &quot;string.h&quot;</span></div>
<div class="line"><a name="l00042"></a><span class="lineno">   42</span>&#160;<span class="preprocessor">#include &quot;error.h&quot;</span></div>
<div class="line"><a name="l00043"></a><span class="lineno">   43</span>&#160;<span class="preprocessor">#include &quot;ctype.h&quot;</span></div>
<div class="line"><a name="l00044"></a><span class="lineno">   44</span>&#160;</div>
<div class="line"><a name="l00045"></a><span class="lineno">   45</span>&#160;<span class="preprocessor">#define TOLERANCE_ORTHO 1e-10</span></div>
<div class="line"><a name="l00046"></a><span class="lineno">   46</span>&#160;<span class="preprocessor"></span></div>
<div class="line"><a name="l00047"></a><span class="lineno">   47</span>&#160;<span class="keyword">namespace </span>MathExtra </div>
<div class="line"><a name="l00048"></a><span class="lineno">   48</span>&#160;{</div>
<div class="line"><a name="l00049"></a><span class="lineno">   49</span>&#160;</div>
<div class="line"><a name="l00050"></a><span class="lineno">   50</span>&#160;<span class="comment">//  inline void     outerProduct(double *vec1, double *vec2, double **m);</span></div>
<div class="line"><a name="l00051"></a><span class="lineno">   51</span>&#160;<span class="comment">//  inline double  spheroidGeometry(int index, double bi, double ai);</span></div>
<div class="line"><a name="l00052"></a><span class="lineno">   52</span>&#160;</div>
<div class="line"><a name="l00053"></a><span class="lineno">   53</span>&#160;</div>
<div class="line"><a name="l00054"></a><span class="lineno">   54</span>&#160;</div>
<div class="line"><a name="l00055"></a><span class="lineno">   55</span>&#160;<span class="comment">//--------------------------------------------------------------------</span></div>
<div class="line"><a name="l00056"></a><span class="lineno">   56</span>&#160;<span class="comment">//   Outer Product of two vectors</span></div>
<div class="line"><a name="l00057"></a><span class="lineno">   57</span>&#160;<span class="keyword">inline</span> <span class="keywordtype">void</span> outerProduct(<span class="keywordtype">double</span> *vec1, <span class="keywordtype">double</span> *vec2, <span class="keywordtype">double</span> **m)</div>
<div class="line"><a name="l00058"></a><span class="lineno">   58</span>&#160;{</div>
<div class="line"><a name="l00059"></a><span class="lineno">   59</span>&#160;  <span class="keywordtype">int</span> i, j;</div>
<div class="line"><a name="l00060"></a><span class="lineno">   60</span>&#160;  <span class="comment">//debug output</span></div>
<div class="line"><a name="l00061"></a><span class="lineno">   61</span>&#160;  <span class="keywordflow">for</span>( i = 0; i &lt; 3; ++i )</div>
<div class="line"><a name="l00062"></a><span class="lineno">   62</span>&#160;<span class="comment">//    printf(&quot;OUTER PRODUCT: Input: vec1 element %d = %g&quot;, i, vec1[i]);</span></div>
<div class="line"><a name="l00063"></a><span class="lineno">   63</span>&#160;  <span class="keywordflow">for</span>( i = 0; i &lt; 3; ++i )</div>
<div class="line"><a name="l00064"></a><span class="lineno">   64</span>&#160;<span class="comment">//    printf(&quot;OUTER PRODUCT: Input: vec2 element %d=%g&quot;, i, vec2[i]);</span></div>
<div class="line"><a name="l00065"></a><span class="lineno">   65</span>&#160;  </div>
<div class="line"><a name="l00066"></a><span class="lineno">   66</span>&#160;  <span class="comment">//calculation</span></div>
<div class="line"><a name="l00067"></a><span class="lineno">   67</span>&#160;  <span class="keywordflow">for</span>( i = 0; i &lt; 3; ++i )</div>
<div class="line"><a name="l00068"></a><span class="lineno">   68</span>&#160;    <span class="keywordflow">for</span>( j = 0; j &lt; 3; ++j )</div>
<div class="line"><a name="l00069"></a><span class="lineno">   69</span>&#160;    {</div>
<div class="line"><a name="l00070"></a><span class="lineno">   70</span>&#160;      m[i][j] = vec1[i] * vec2[j];</div>
<div class="line"><a name="l00071"></a><span class="lineno">   71</span>&#160;      printf(<span class="stringliteral">&quot;OUTER PRODUCT: Result: m[%d][%d]=%g&quot;</span>, i, j, m[i][j]);</div>
<div class="line"><a name="l00072"></a><span class="lineno">   72</span>&#160;    }</div>
<div class="line"><a name="l00073"></a><span class="lineno">   73</span>&#160;    </div>
<div class="line"><a name="l00074"></a><span class="lineno">   74</span>&#160;    </div>
<div class="line"><a name="l00075"></a><span class="lineno">   75</span>&#160;}</div>
<div class="line"><a name="l00076"></a><span class="lineno">   76</span>&#160;<span class="comment">//--------------------------------------------------------------------</span></div>
<div class="line"><a name="l00077"></a><span class="lineno">   77</span>&#160;<span class="comment">// Compute the major, minor axis and eccentricity parameters of a prolate spheroid</span></div>
<div class="line"><a name="l00078"></a><span class="lineno">   78</span>&#160;<span class="keyword">inline</span> <span class="keywordtype">bool</span> spheroidGeometry(<span class="keywordtype">double</span> radius, <span class="keywordtype">double</span> aspectRatio,  <span class="comment">//inputs</span></div>
<div class="line"><a name="l00079"></a><span class="lineno">   79</span>&#160;                                 <span class="keywordtype">double</span>&amp; ai,    <span class="keywordtype">double</span>&amp; bi,              <span class="comment">//outputs</span></div>
<div class="line"><a name="l00080"></a><span class="lineno">   80</span>&#160;                                 <span class="keywordtype">double</span>&amp; ei,    <span class="keywordtype">double</span>&amp; Le              <span class="comment">//outputs</span></div>
<div class="line"><a name="l00081"></a><span class="lineno">   81</span>&#160;                                ) <span class="comment">//</span></div>
<div class="line"><a name="l00082"></a><span class="lineno">   82</span>&#160;{</div>
<div class="line"><a name="l00083"></a><span class="lineno">   83</span>&#160;    <span class="comment">//INPUT</span></div>
<div class="line"><a name="l00084"></a><span class="lineno">   84</span>&#160;    <span class="comment">//  radius      ...volume-equivalent radius of the spheroid</span></div>
<div class="line"><a name="l00085"></a><span class="lineno">   85</span>&#160;    <span class="comment">//  aspectRatio ...major/minor aspect ratio</span></div>
<div class="line"><a name="l00086"></a><span class="lineno">   86</span>&#160;    </div>
<div class="line"><a name="l00087"></a><span class="lineno">   87</span>&#160;    <span class="comment">//OUTPUT</span></div>
<div class="line"><a name="l00088"></a><span class="lineno">   88</span>&#160;    <span class="comment">//  ai  ... </span></div>
<div class="line"><a name="l00089"></a><span class="lineno">   89</span>&#160;    <span class="comment">//  bi  ... </span></div>
<div class="line"><a name="l00090"></a><span class="lineno">   90</span>&#160;    <span class="comment">//  ei  ... </span></div>
<div class="line"><a name="l00091"></a><span class="lineno">   91</span>&#160;    <span class="comment">//  Le  ... </span></div>
<div class="line"><a name="l00092"></a><span class="lineno">   92</span>&#160;  </div>
<div class="line"><a name="l00093"></a><span class="lineno">   93</span>&#160;    <span class="keywordflow">if</span>(radius&lt;=0.0)     <span class="comment">//avoid troubles in case radius is 0 or negative</span></div>
<div class="line"><a name="l00094"></a><span class="lineno">   94</span>&#160;        <span class="keywordflow">return</span> <span class="keyword">false</span>;</div>
<div class="line"><a name="l00095"></a><span class="lineno">   95</span>&#160;</div>
<div class="line"><a name="l00096"></a><span class="lineno">   96</span>&#160;        ai = radius * std::pow(aspectRatio*aspectRatio,0.33333333333333333333333);</div>
<div class="line"><a name="l00097"></a><span class="lineno">   97</span>&#160;    bi = ai / aspectRatio;</div>
<div class="line"><a name="l00098"></a><span class="lineno">   98</span>&#160;        ei = std::sqrt( </div>
<div class="line"><a name="l00099"></a><span class="lineno">   99</span>&#160;                        1.0</div>
<div class="line"><a name="l00100"></a><span class="lineno">  100</span>&#160;                   - 1.0 / (aspectRatio*aspectRatio)</div>
<div class="line"><a name="l00101"></a><span class="lineno">  101</span>&#160;                      );</div>
<div class="line"><a name="l00102"></a><span class="lineno">  102</span>&#160;        Le = std::log(</div>
<div class="line"><a name="l00103"></a><span class="lineno">  103</span>&#160;                           (1.0+ei)</div>
<div class="line"><a name="l00104"></a><span class="lineno">  104</span>&#160;                          /(1.0-ei)</div>
<div class="line"><a name="l00105"></a><span class="lineno">  105</span>&#160;                 );</div>
<div class="line"><a name="l00106"></a><span class="lineno">  106</span>&#160;</div>
<div class="line"><a name="l00107"></a><span class="lineno">  107</span>&#160;        <span class="keywordflow">return</span> <span class="keyword">true</span>;                </div>
<div class="line"><a name="l00108"></a><span class="lineno">  108</span>&#160;}</div>
<div class="line"><a name="l00109"></a><span class="lineno">  109</span>&#160;</div>
<div class="line"><a name="l00110"></a><span class="lineno">  110</span>&#160;<span class="comment">//--------------------------------------------------------------------</span></div>
<div class="line"><a name="l00111"></a><span class="lineno">  111</span>&#160;<span class="comment">// Compute the major, minor axis and eccentricity parameters of a prolate spheroid</span></div>
<div class="line"><a name="l00112"></a><span class="lineno">  112</span>&#160;<span class="keyword">inline</span> <span class="keywordtype">double</span> Pi()</div>
<div class="line"><a name="l00113"></a><span class="lineno">  113</span>&#160;{</div>
<div class="line"><a name="l00114"></a><span class="lineno">  114</span>&#160;    <span class="keywordflow">return</span> 3.1415926535897932384626433832795;</div>
<div class="line"><a name="l00115"></a><span class="lineno">  115</span>&#160;}</div>
<div class="line"><a name="l00116"></a><span class="lineno">  116</span>&#160;</div>
<div class="line"><a name="l00117"></a><span class="lineno">  117</span>&#160;</div>
<div class="line"><a name="l00118"></a><span class="lineno">  118</span>&#160;<span class="comment">//--------------------------------------------------------------------</span></div>
<div class="line"><a name="l00119"></a><span class="lineno">  119</span>&#160;<span class="comment">// Compute the major, minor axis and eccentricity parameters of a prolate spheroid</span></div>
<div class="line"><a name="l00120"></a><span class="lineno">  120</span>&#160;<span class="keyword">inline</span> <span class="keywordtype">bool</span> spheroidGeometry2(<span class="keywordtype">double</span> radius, <span class="keywordtype">double</span> aspectRatio,  <span class="comment">//inputs</span></div>
<div class="line"><a name="l00121"></a><span class="lineno">  121</span>&#160;                                 <span class="keywordtype">double</span>&amp; ai,     <span class="keywordtype">double</span>&amp; bi,           <span class="comment">//outputs</span></div>
<div class="line"><a name="l00122"></a><span class="lineno">  122</span>&#160;                                 <span class="keywordtype">double</span>&amp; XAe,    <span class="keywordtype">double</span>&amp; YAe,         <span class="comment">//outputs</span></div>
<div class="line"><a name="l00123"></a><span class="lineno">  123</span>&#160;                                 <span class="keywordtype">double</span>&amp; XCe,    <span class="keywordtype">double</span>&amp; YCe,         <span class="comment">//outputs</span></div>
<div class="line"><a name="l00124"></a><span class="lineno">  124</span>&#160;                                 <span class="keywordtype">double</span>&amp; YHe</div>
<div class="line"><a name="l00125"></a><span class="lineno">  125</span>&#160;                                ) <span class="comment">//</span></div>
<div class="line"><a name="l00126"></a><span class="lineno">  126</span>&#160;{</div>
<div class="line"><a name="l00127"></a><span class="lineno">  127</span>&#160;    <span class="comment">//INPUT</span></div>
<div class="line"><a name="l00128"></a><span class="lineno">  128</span>&#160;    <span class="comment">//  radius      ...volume-equivalent radius of the spheroid</span></div>
<div class="line"><a name="l00129"></a><span class="lineno">  129</span>&#160;    <span class="comment">//  aspectRatio ...major/minor aspect ratio</span></div>
<div class="line"><a name="l00130"></a><span class="lineno">  130</span>&#160;    </div>
<div class="line"><a name="l00131"></a><span class="lineno">  131</span>&#160;    <span class="comment">//OUTPUT</span></div>
<div class="line"><a name="l00132"></a><span class="lineno">  132</span>&#160;    <span class="comment">//  XAe  ...Eccentricity dependet parameter</span></div>
<div class="line"><a name="l00133"></a><span class="lineno">  133</span>&#160;    <span class="comment">//  YAe  ...Eccentricity dependet parameter</span></div>
<div class="line"><a name="l00134"></a><span class="lineno">  134</span>&#160;    <span class="comment">//  XCe  ...Eccentricity dependet parameter</span></div>
<div class="line"><a name="l00135"></a><span class="lineno">  135</span>&#160;    <span class="comment">//  XCe  ...Eccentricity dependet parameter</span></div>
<div class="line"><a name="l00136"></a><span class="lineno">  136</span>&#160;    <span class="comment">//  YCe  ...Eccentricity dependet parameter</span></div>
<div class="line"><a name="l00137"></a><span class="lineno">  137</span>&#160;    <span class="comment">//  YHe  ...Eccentricity dependet parameter</span></div>
<div class="line"><a name="l00138"></a><span class="lineno">  138</span>&#160;  </div>
<div class="line"><a name="l00139"></a><span class="lineno">  139</span>&#160;</div>
<div class="line"><a name="l00140"></a><span class="lineno">  140</span>&#160;    <span class="keywordtype">double</span> ei(0.0), Le(0.0);  </div>
<div class="line"><a name="l00141"></a><span class="lineno">  141</span>&#160;    <span class="keywordtype">bool</span>   result = </div>
<div class="line"><a name="l00142"></a><span class="lineno">  142</span>&#160;          spheroidGeometry(radius, aspectRatio,  <span class="comment">//inputs</span></div>
<div class="line"><a name="l00143"></a><span class="lineno">  143</span>&#160;                                 ai,     bi,              <span class="comment">//outputs</span></div>
<div class="line"><a name="l00144"></a><span class="lineno">  144</span>&#160;                                 ei,    Le              <span class="comment">//outputs</span></div>
<div class="line"><a name="l00145"></a><span class="lineno">  145</span>&#160;                              );</div>
<div class="line"><a name="l00146"></a><span class="lineno">  146</span>&#160;    <span class="keywordflow">if</span>(!result)</div>
<div class="line"><a name="l00147"></a><span class="lineno">  147</span>&#160;        <span class="keywordflow">return</span> <span class="keyword">false</span>;</div>
<div class="line"><a name="l00148"></a><span class="lineno">  148</span>&#160;        </div>
<div class="line"><a name="l00149"></a><span class="lineno">  149</span>&#160;    XAe= 2.6666666666666666666666667</div>
<div class="line"><a name="l00150"></a><span class="lineno">  150</span>&#160;         *ei*ei*ei</div>
<div class="line"><a name="l00151"></a><span class="lineno">  151</span>&#160;         /(-2.0*ei+(1.0+ei*ei)*Le); </div>
<div class="line"><a name="l00152"></a><span class="lineno">  152</span>&#160;    YAe= 5.333333333333333333333333333</div>
<div class="line"><a name="l00153"></a><span class="lineno">  153</span>&#160;        *ei*ei*ei</div>
<div class="line"><a name="l00154"></a><span class="lineno">  154</span>&#160;        /(2.0*ei+(3*ei*ei-1.0)*Le);</div>
<div class="line"><a name="l00155"></a><span class="lineno">  155</span>&#160;    XCe= 1.333333333333333333333333333</div>
<div class="line"><a name="l00156"></a><span class="lineno">  156</span>&#160;        *ei*ei*ei</div>
<div class="line"><a name="l00157"></a><span class="lineno">  157</span>&#160;        *(1.0-ei*ei)</div>
<div class="line"><a name="l00158"></a><span class="lineno">  158</span>&#160;        /(2.0*ei-(1.0-ei*ei)*Le);</div>
<div class="line"><a name="l00159"></a><span class="lineno">  159</span>&#160;    YCe= 1.3333333333333333333333</div>
<div class="line"><a name="l00160"></a><span class="lineno">  160</span>&#160;        *ei*ei*ei</div>
<div class="line"><a name="l00161"></a><span class="lineno">  161</span>&#160;        *(2.0-ei*ei)</div>
<div class="line"><a name="l00162"></a><span class="lineno">  162</span>&#160;        /(-2.0*ei+(1.0+ei*ei)*Le);</div>
<div class="line"><a name="l00163"></a><span class="lineno">  163</span>&#160;    YHe= 1.3333333333333333333333</div>
<div class="line"><a name="l00164"></a><span class="lineno">  164</span>&#160;        *ei*ei*ei*ei*ei</div>
<div class="line"><a name="l00165"></a><span class="lineno">  165</span>&#160;        /(-2.0*ei+(1.0+ei*ei)*Le);</div>
<div class="line"><a name="l00166"></a><span class="lineno">  166</span>&#160;</div>
<div class="line"><a name="l00167"></a><span class="lineno">  167</span>&#160;        <span class="keywordflow">return</span> <span class="keyword">true</span>;                </div>
<div class="line"><a name="l00168"></a><span class="lineno">  168</span>&#160;</div>
<div class="line"><a name="l00169"></a><span class="lineno">  169</span>&#160;}</div>
<div class="line"><a name="l00170"></a><span class="lineno">  170</span>&#160;</div>
<div class="line"><a name="l00171"></a><span class="lineno">  171</span>&#160;<span class="comment">//--------------------------------------------------------------------</span></div>
<div class="line"><a name="l00172"></a><span class="lineno">  172</span>&#160;<span class="comment">// zeroize a 3x3x3 tensor</span></div>
<div class="line"><a name="l00173"></a><span class="lineno">  173</span>&#160;<span class="keyword">inline</span> <span class="keywordtype">void</span> zeroize333(<span class="keywordtype">double</span> tensor[3][3][3] )</div>
<div class="line"><a name="l00174"></a><span class="lineno">  174</span>&#160;{</div>
<div class="line"><a name="l00175"></a><span class="lineno">  175</span>&#160;    <span class="keywordflow">for</span>(<span class="keywordtype">int</span> iX=0; iX&lt;3; iX++)</div>
<div class="line"><a name="l00176"></a><span class="lineno">  176</span>&#160;        <span class="keywordflow">for</span>(<span class="keywordtype">int</span> iY=0; iY&lt;3; iY++)</div>
<div class="line"><a name="l00177"></a><span class="lineno">  177</span>&#160;            <span class="keywordflow">for</span>(<span class="keywordtype">int</span> iZ=0; iZ&lt;3; iZ++)</div>
<div class="line"><a name="l00178"></a><span class="lineno">  178</span>&#160;                tensor[iX][iY][iZ] = 0.0;</div>
<div class="line"><a name="l00179"></a><span class="lineno">  179</span>&#160;}</div>
<div class="line"><a name="l00180"></a><span class="lineno">  180</span>&#160;</div>
<div class="line"><a name="l00181"></a><span class="lineno">  181</span>&#160;<span class="comment">//--------------------------------------------------------------------</span></div>
<div class="line"><a name="l00182"></a><span class="lineno">  182</span>&#160;<span class="comment">// zeroize a 3x3 tensor</span></div>
<div class="line"><a name="l00183"></a><span class="lineno">  183</span>&#160;<span class="keyword">inline</span> <span class="keywordtype">void</span> zeroize33(<span class="keywordtype">double</span> tensor[3][3] )</div>
<div class="line"><a name="l00184"></a><span class="lineno">  184</span>&#160;{</div>
<div class="line"><a name="l00185"></a><span class="lineno">  185</span>&#160;    <span class="keywordflow">for</span>(<span class="keywordtype">int</span> iX=0; iX&lt;3; iX++)</div>
<div class="line"><a name="l00186"></a><span class="lineno">  186</span>&#160;        <span class="keywordflow">for</span>(<span class="keywordtype">int</span> iY=0; iY&lt;3; iY++)</div>
<div class="line"><a name="l00187"></a><span class="lineno">  187</span>&#160;                tensor[iX][iY] = 0.0;</div>
<div class="line"><a name="l00188"></a><span class="lineno">  188</span>&#160;}</div>
<div class="line"><a name="l00189"></a><span class="lineno">  189</span>&#160;</div>
<div class="line"><a name="l00190"></a><span class="lineno">  190</span>&#160;<span class="comment">//--------------------------------------------------------------------</span></div>
<div class="line"><a name="l00191"></a><span class="lineno">  191</span>&#160;<span class="comment">// multiply a 3x3x3 tensor with a scalar</span></div>
<div class="line"><a name="l00192"></a><span class="lineno">  192</span>&#160;<span class="keyword">inline</span> <span class="keywordtype">void</span> multiply333(<span class="keywordtype">double</span> scalar, <span class="keywordtype">double</span> tensor[3][3][3] )</div>
<div class="line"><a name="l00193"></a><span class="lineno">  193</span>&#160;{</div>
<div class="line"><a name="l00194"></a><span class="lineno">  194</span>&#160;    <span class="keywordflow">for</span>(<span class="keywordtype">int</span> iX=0; iX&lt;3; iX++)</div>
<div class="line"><a name="l00195"></a><span class="lineno">  195</span>&#160;        <span class="keywordflow">for</span>(<span class="keywordtype">int</span> iY=0; iY&lt;3; iY++)</div>
<div class="line"><a name="l00196"></a><span class="lineno">  196</span>&#160;            <span class="keywordflow">for</span>(<span class="keywordtype">int</span> iZ=0; iZ&lt;3; iZ++)</div>
<div class="line"><a name="l00197"></a><span class="lineno">  197</span>&#160;                tensor[iX][iY][iZ] *= scalar;</div>
<div class="line"><a name="l00198"></a><span class="lineno">  198</span>&#160;}</div>
<div class="line"><a name="l00199"></a><span class="lineno">  199</span>&#160;<span class="comment">//--------------------------------------------------------------------</span></div>
<div class="line"><a name="l00200"></a><span class="lineno">  200</span>&#160;<span class="comment">// Compute a dot and dyadic product of with a vector</span></div>
<div class="line"><a name="l00201"></a><span class="lineno">  201</span>&#160;<span class="keyword">inline</span> <span class="keywordtype">void</span> permutationTensor(<span class="keywordtype">double</span> tensor[3][3][3] )</div>
<div class="line"><a name="l00202"></a><span class="lineno">  202</span>&#160;{</div>
<div class="line"><a name="l00203"></a><span class="lineno">  203</span>&#160;    zeroize333(tensor);</div>
<div class="line"><a name="l00204"></a><span class="lineno">  204</span>&#160;    tensor[0][1][2] = 1.0; </div>
<div class="line"><a name="l00205"></a><span class="lineno">  205</span>&#160;    tensor[1][2][0] = 1.0; </div>
<div class="line"><a name="l00206"></a><span class="lineno">  206</span>&#160;    tensor[2][0][1] = 1.0; </div>
<div class="line"><a name="l00207"></a><span class="lineno">  207</span>&#160;    tensor[0][2][1] =-1.0; </div>
<div class="line"><a name="l00208"></a><span class="lineno">  208</span>&#160;    tensor[2][1][0] =-1.0; </div>
<div class="line"><a name="l00209"></a><span class="lineno">  209</span>&#160;    tensor[1][0][2] =-1.0; </div>
<div class="line"><a name="l00210"></a><span class="lineno">  210</span>&#160;}</div>
<div class="line"><a name="l00211"></a><span class="lineno">  211</span>&#160;</div>
<div class="line"><a name="l00212"></a><span class="lineno">  212</span>&#160;</div>
<div class="line"><a name="l00213"></a><span class="lineno">  213</span>&#160;</div>
<div class="line"><a name="l00214"></a><span class="lineno">  214</span>&#160;<span class="comment">//--------------------------------------------------------------------</span></div>
<div class="line"><a name="l00215"></a><span class="lineno">  215</span>&#160;<span class="comment">// Compute a dot product of the permutation tensor and </span></div>
<div class="line"><a name="l00216"></a><span class="lineno">  216</span>&#160;<span class="comment">// then a dyadic product of with a vector</span></div>
<div class="line"><a name="l00217"></a><span class="lineno">  217</span>&#160;<span class="keyword">inline</span> <span class="keywordtype">bool</span> permutationDotDyadic( </div>
<div class="line"><a name="l00218"></a><span class="lineno">  218</span>&#160;                                 <span class="keywordtype">double</span> vector[3], </div>
<div class="line"><a name="l00219"></a><span class="lineno">  219</span>&#160;                                 <span class="keywordtype">double</span>  tensor[3][3][3]      </div>
<div class="line"><a name="l00220"></a><span class="lineno">  220</span>&#160;                                )</div>
<div class="line"><a name="l00221"></a><span class="lineno">  221</span>&#160;{</div>
<div class="line"><a name="l00222"></a><span class="lineno">  222</span>&#160;    <span class="comment">//Generate permutation tensor</span></div>
<div class="line"><a name="l00223"></a><span class="lineno">  223</span>&#160;    <span class="keywordtype">double</span> permutationT[3][3][3];</div>
<div class="line"><a name="l00224"></a><span class="lineno">  224</span>&#160;    permutationTensor(permutationT);</div>
<div class="line"><a name="l00225"></a><span class="lineno">  225</span>&#160;    </div>
<div class="line"><a name="l00226"></a><span class="lineno">  226</span>&#160;    <span class="comment">//Step 1: compute dot prodcut of permutation tensor</span></div>
<div class="line"><a name="l00227"></a><span class="lineno">  227</span>&#160;    <span class="keywordtype">double</span> permutationDotProd[3][3];</div>
<div class="line"><a name="l00228"></a><span class="lineno">  228</span>&#160;    zeroize33(permutationDotProd);</div>
<div class="line"><a name="l00229"></a><span class="lineno">  229</span>&#160;</div>
<div class="line"><a name="l00230"></a><span class="lineno">  230</span>&#160;    <span class="keywordflow">for</span>(<span class="keywordtype">int</span> iX=0; iX&lt;3; iX++)</div>
<div class="line"><a name="l00231"></a><span class="lineno">  231</span>&#160;        <span class="keywordflow">for</span>(<span class="keywordtype">int</span> iY=0; iY&lt;3; iY++)</div>
<div class="line"><a name="l00232"></a><span class="lineno">  232</span>&#160;            <span class="keywordflow">for</span>(<span class="keywordtype">int</span> iZ=0; iZ&lt;3; iZ++)</div>
<div class="line"><a name="l00233"></a><span class="lineno">  233</span>&#160;                permutationDotProd[iX][iY] += permutationT[iX][iY][iZ]</div>
<div class="line"><a name="l00234"></a><span class="lineno">  234</span>&#160;                                            * vector[iZ];</div>
<div class="line"><a name="l00235"></a><span class="lineno">  235</span>&#160;</div>
<div class="line"><a name="l00236"></a><span class="lineno">  236</span>&#160;    <span class="keywordflow">for</span>(<span class="keywordtype">int</span> iX=0; iX&lt;3; iX++)</div>
<div class="line"><a name="l00237"></a><span class="lineno">  237</span>&#160;        <span class="keywordflow">for</span>(<span class="keywordtype">int</span> iY=0; iY&lt;3; iY++)</div>
<div class="line"><a name="l00238"></a><span class="lineno">  238</span>&#160;            <span class="keywordflow">for</span>(<span class="keywordtype">int</span> iZ=0; iZ&lt;3; iZ++)</div>
<div class="line"><a name="l00239"></a><span class="lineno">  239</span>&#160;                tensor[iX][iY][iZ] = permutationDotProd[iX][iY]</div>
<div class="line"><a name="l00240"></a><span class="lineno">  240</span>&#160;                                   * vector[iZ]; </div>
<div class="line"><a name="l00241"></a><span class="lineno">  241</span>&#160;    <span class="keywordflow">return</span> <span class="keyword">true</span>;</div>
<div class="line"><a name="l00242"></a><span class="lineno">  242</span>&#160;</div>
<div class="line"><a name="l00243"></a><span class="lineno">  243</span>&#160;}</div>
<div class="line"><a name="l00244"></a><span class="lineno">  244</span>&#160;</div>
<div class="line"><a name="l00245"></a><span class="lineno">  245</span>&#160;<span class="comment">//--------------------------------------------------------------------</span></div>
<div class="line"><a name="l00246"></a><span class="lineno">  246</span>&#160;<span class="comment">// Compute a dot and dyadic product of with a vector</span></div>
<div class="line"><a name="l00247"></a><span class="lineno">  247</span>&#160;<span class="keyword">inline</span> <span class="keywordtype">bool</span> doubleDotTensor333Tensor33(<span class="keywordtype">double</span> tensor333[3][3][3], </div>
<div class="line"><a name="l00248"></a><span class="lineno">  248</span>&#160;                                       <span class="keywordtype">double</span> tensor33[3][3],</div>
<div class="line"><a name="l00249"></a><span class="lineno">  249</span>&#160;                                       <span class="keywordtype">double</span> result[3]</div>
<div class="line"><a name="l00250"></a><span class="lineno">  250</span>&#160;                                      )</div>
<div class="line"><a name="l00251"></a><span class="lineno">  251</span>&#160;{</div>
<div class="line"><a name="l00252"></a><span class="lineno">  252</span>&#160;    result[0]=0.0;result[1]=0.0;result[2]=0.0;</div>
<div class="line"><a name="l00253"></a><span class="lineno">  253</span>&#160;    </div>
<div class="line"><a name="l00254"></a><span class="lineno">  254</span>&#160;    <span class="keywordflow">for</span>(<span class="keywordtype">int</span> iX=0; iX&lt;3; iX++)</div>
<div class="line"><a name="l00255"></a><span class="lineno">  255</span>&#160;        <span class="keywordflow">for</span>(<span class="keywordtype">int</span> iY=0; iY&lt;3; iY++)</div>
<div class="line"><a name="l00256"></a><span class="lineno">  256</span>&#160;            <span class="keywordflow">for</span>(<span class="keywordtype">int</span> iZ=0; iZ&lt;3; iZ++)</div>
<div class="line"><a name="l00257"></a><span class="lineno">  257</span>&#160;                result[iX] += tensor333[iX][iY][iZ] * tensor33[iY][iZ];</div>
<div class="line"><a name="l00258"></a><span class="lineno">  258</span>&#160;</div>
<div class="line"><a name="l00259"></a><span class="lineno">  259</span>&#160;    <span class="keywordflow">return</span> <span class="keyword">true</span>;</div>
<div class="line"><a name="l00260"></a><span class="lineno">  260</span>&#160;}</div>
<div class="line"><a name="l00261"></a><span class="lineno">  261</span>&#160;</div>
<div class="line"><a name="l00262"></a><span class="lineno">  262</span>&#160;</div>
<div class="line"><a name="l00263"></a><span class="lineno">  263</span>&#160;}; <span class="comment">//end of namespace</span></div>
<div class="line"><a name="l00264"></a><span class="lineno">  264</span>&#160;</div>
<div class="line"><a name="l00265"></a><span class="lineno">  265</span>&#160;<span class="preprocessor">#endif</span></div>
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